Linear algebra

The Linear Algebra module provides comprehensive tools for performing matrix and vector computations in Nelson.

It includes functions for matrix factorization, decomposition, inversion, and analysis, as well as operations on eigenvalues, singular values, and subspaces.

The module supports advanced numerical methods for evaluating matrix properties, condition numbers, and transformations, enabling efficient and accurate solutions for a wide range of linear algebra problems.

Functions

• balance - Diagonal scaling to improve eigenvalue accuracy.

• bandwidth - Lower and upper matrix bandwidth.

• chol - Cholesky factorization.

• cond - Condition number for inversion.

• condeig - Condition number with respect to eigenvalues.

• det - Matrix determinant.

• diff - Differences and approximate derivatives.

• eig - Eigenvalues and eigenvectors.

• expm - Computes the matrix exponential of a square matrix.

• gradient - Numerical gradient.

• inv - Matrix inverse.

• isbanded - Determine if matrix is within specific bandwidth.

• ishermitian - Computes if matrix is hermitian or skew-hermitian.

• issymmetric - Computes if matrix is symmetric.

• kron - Kronecker tensor product.

• logm - Computes the matrix logarithm of a square matrix.

• lu - LU matrix factorization.

• orth - Range space of a matrix.

• planerot - Givens plane rotation.

• rank - Rank of matrix.

• rcond - Inverse condition number.

• rref - Gauss-Jordan elimination.

• rsf2csf - Convert real Schur form to complex Schur form.

• schur - Schur decomposition.

• sqrtm - Computes the matrix square root of a square matrix.

• subspace - Angle between two subspaces.

• svd - Singular Value Decomposition.

• trace - Matrix trace.

• vecnorm - Vector-wise norm.